Interference rejection combining with reduced complexity

ABSTRACT

A method and apparatus comprises acquiring set of input streams associated with a spatial layer configured for a terminal device, and estimating a channel vector h representing a radio channel response associated with the spatial layer. An interference covariance matrix R representing power of interference is computed from at least one other spatial layer in the set of input streams and correlation of the interference within the set of input streams of the spatial layer. A per-layer interference rejection is performed, combining equalization on the set of input streams, comprising: a) estimating x=R−1h as a combination of a set of linear equations, wherein the number of linear equations is defined by an input parameter to be equal to or smaller than dimensions of the interference covariance matrix; and b) computing an estimate of a transmitted symbol on the basis of the channel vector and the estimated x.

CROSS REFERENCE TO RELATED APPLICATION

This application claims the benefit of Finnish Patent Application No.20225464, filed May 27, 2022. The entire content of the above-referencedapplication is hereby incorporated by reference.

FIELD

Various embodiments described herein relate to the field of wirelesscommunications and, particularly, to performing interference rejectioncombining in a multiple-input-multiple-output (MIMO) receiver.

BACKGROUND

Interference rejection combining (IRC) techniques are widely applied formitigating co-channel interference. In particular, cellularcommunication systems employ IRC reception methods. The IRCs may beapplied to multi-beam reception techniques such as MIMO communications.A benefit of an IRC receiver is that it does not need detailedinformation about interfering signals, such as radio channel propagationcharacteristics. Therefore, IRC receivers are simple compared to otherreceiver architectures. As known in the art, a characteristic of an IRCreceiver is computation of a covariance matrix representing covariancebetween a desired signal and the interfering signals. Inversion of thecovariance matrix is also a characteristic of the IRC receiver, and theinversion operation is computationally complex.

XIAO, C. et al. Low-complexity soft-output detection for massive MIMOusing SCBiCG and Lanczos methods. In: China Communications. IEEE[online], December 2015, Vol. 12, pages 9-17 discloses a minimum meansquare error (MMSE) detection scheme for uplink massive MIMO systemsutilizing the symmetric complex bi-conjugate gradients (SCBiCG) and theLanczos method.

QU, H. et al. Efficient Channel Equalization and Symbol Detection forMIMO OTFS Systems. In: IEEE Transactions on Wireless Communications.IEEE [online], February 2022, Vol. 21, No. 8, pages 6672-6686 disclosesa time-space domain channel equalizer for MIMO over orthogonal timefrequency space (OTFS) modulation, relying on the mathematical leastsquares minimum residual algorithm, to remove the channel distortion ondata symbols.

BRIEF DESCRIPTION

Some aspects of the invention are defined by the independent claims.

Some embodiments of the invention are defined in the dependent claims.

The embodiments and features, if any, described in this specificationthat do not fall under the scope of the independent claims are to beinterpreted as examples useful for understanding various embodiments ofthe invention. Some aspects of the disclosure are defined by theindependent claims.

According to an aspect, there is provided an apparatus comprising meansfor performing: acquiring set of input streams associated with a spatiallayer configured for a terminal device; estimating, on the basis of areference signal, a channel vector h representing a radio channelresponse associated with the spatial layer; computing an interferencecovariance matrix R representing power of interference from at least oneother spatial layer in the set of input streams and correlation of theinterference within the set of input streams of the spatial layer;performing a per-layer interference rejection combining equalization onthe set of input streams, comprising:

-   -   a) estimating x=R⁻¹h as a combination of a set of linear        equations, wherein the number of linear equations is defined by        an input parameter to be equal to or smaller than dimensions of        the interference covariance matrix; and    -   b) computing an estimate of a transmitted symbol on the basis of        the channel vector and the estimated x.

In an embodiment, the input parameter is dependent on at least one of anumber of input streams in the set of input streams, a modulation andcoding scheme of the spatial layer, and a total number of spatial layersconfigured for all terminal devices scheduled to the same time-frequencyresources as the terminal device.

In an embodiment, the input parameter is dependent on the number ofinput streams, the modulation and coding scheme of the spatial layer,and the total number of spatial layers, and wherein values of the inputparameter are directly proportional with an order of the modulation andcoding scheme, directly proportional to the number of spatial layers,and inversely proportional to the number of input streams.

In an embodiment, the set of linear equations defines a Krylov sub-spacepresentation comprising orthonormal basis vectors defining the Krylovsub-space, wherein the input parameter defines the number of saidorthonormal basis vectors.

In an embodiment, the Krylov sub-space presentation further compriseselements of a real-valued tridiagonal matrix, and wherein step b)comprises inversion of the real-valued tridiagonal matrix.

In an embodiment, the means are configured to perform the inversion ofthe real-value tridiagonal matrix when solving weights for theorthonormal basis vectors by using Thomas algorithm, to combine theweights with the respective orthonormal basis vectors and with aninitial estimate, and to compute the estimate of the transmitted symbolon the basis of said combining.

In an embodiment, the means are configured to perform the inversion ofthe real-value tridiagonal matrix when solving weights for theorthonormal basis vectors by computing an eigenvalue decomposition ofthe tridiagonal matrix, to compute the weights by inverting eigenvaluesof the eigenvalue decomposition, to combine the weights with therespective orthonormal basis vectors and with an initial estimate, andto compute the estimate of the transmitted symbol on the basis of saidcombining.

In an embodiment, the means are configured to use the initial estimatex₀=h./diag(R) in step b), wherein ./ represents element-wise divisionoperation.

In an embodiment, the means are configured to generate the Krylovsub-space presentation by using Lanczos algorithm.

In an embodiment, the means are configured to interpolate the estimatedx or a parameter derived from x to time-frequency resources not carryingthe reference signal.

In an embodiment, the means are configured to average in a determinednumber of channel estimates, wherein the determined number is a functionof a modulation and coding scheme associated with the spatial layer.

In an embodiment, the determined number is smaller for a firstmodulation scheme than for a second modulation scheme, wherein the firstmodulation scheme maps a greater number of bits per symbol than thesecond modulation scheme.

In an embodiment, the means comprise at least one processor and at leastone memory including computer program code, the at least one memory andcomputer program code configured to, with the at least one processor,cause the performance of the apparatus.

According to an aspect, there is provided a method comprising: acquiringset of input streams associated with a spatial layer configured for aterminal device; estimating, on the basis of a reference signal, achannel vector h representing a radio channel response associated withthe spatial layer; computing an interference covariance matrix Rrepresenting power of interference from at least one other spatial layerin the set of input streams and correlation of the interference withinthe set of input streams of the spatial layer; performing a per-layerinterference rejection combining equalization on the set of inputstreams, comprising:

-   -   a) estimating x=R⁻¹h as a combination of a set of linear        equations, wherein the number of linear equations is defined by        an input parameter to be equal to or smaller than dimensions of        the interference covariance matrix; and    -   b) computing an estimate of a transmitted symbol on the basis of        the channel vector and the estimated x.

In an embodiment, the input parameter is dependent on at least one of anumber of input streams in the set of input streams, a modulation andcoding scheme of the spatial layer, and a total number of spatial layersconfigured for all terminal devices scheduled to the same time-frequencyresources as the terminal device.

In an embodiment, the input parameter is dependent on the number ofinput streams, the modulation and coding scheme of the spatial layer,and the total number of spatial layers, and wherein values of the inputparameter are directly proportional with an order of the modulation andcoding scheme, directly proportional to the number of spatial layers,and inversely proportional to the number of input streams.

In an embodiment, the set of linear equations defines a Krylov sub-spacepresentation comprising orthonormal basis vectors defining the Krylovsub-space, wherein the input parameter defines the number of saidorthonormal basis vectors.

In an embodiment, the Krylov sub-space presentation further compriseselements of a real-valued tridiagonal matrix, and wherein step b)comprises inversion of the real-valued tridiagonal matrix.

In an embodiment, the method comprises performing the inversion of thereal-value tridiagonal matrix when solving weights for the orthonormalbasis vectors by using Thomas algorithm, combining the weights with therespective orthonormal basis vectors and with an initial estimate, andcomputing the estimate of the transmitted symbol on the basis of saidcombining.

In an embodiment, the method comprises performing the inversion of thereal-value tridiagonal matrix when solving weights for the orthonormalbasis vectors by computing an eigenvalue decomposition of thetridiagonal matrix, computing the weights by inverting eigenvalues ofthe eigenvalue decomposition, combining the weights with the respectiveorthonormal basis vectors and with an initial estimate, and computingthe estimate of the transmitted symbol on the basis of said combining.

In an embodiment, the method comprises using the initial estimatex₀=h./diag(R) in step b), wherein ./ represents element-wise divisionoperation.

In an embodiment, the method comprises generating the Krylov sub-spacepresentation by using Lanczos algorithm.

In an embodiment, the method comprises interpolating the estimated x ora parameter derived from x to time-frequency resources not carrying thereference signal.

In an embodiment, the method comprises averaging a determined number ofchannel estimates, wherein the determined number is a function of amodulation and coding scheme associated with the spatial layer.

In an embodiment, the determined number is smaller for a firstmodulation scheme than for a second modulation scheme, wherein the firstmodulation scheme maps a greater number of bits per symbol than thesecond modulation scheme.

According to an aspect, there is provided a computer program productembodied on a computer-readable medium and comprising a computer programcode readable by a computer, wherein the computer program codeconfigures the computer to carry out a computer process comprising:acquiring set of input streams associated with a spatial layerconfigured for a terminal device; estimating, on the basis of areference signal, a channel vector h representing a radio channelresponse associated with the spatial layer; computing an interferencecovariance matrix R representing power of interference from at least oneother spatial layer in the set of input streams and correlation of theinterference within the set of input streams of the spatial layer;performing a per-layer interference rejection combining equalization onthe set of input streams, comprising:

-   -   a) estimating x=R⁻¹h as a combination of a set of linear        equations, wherein the number of linear equations is defined by        an input parameter to be equal to or smaller than dimensions of        the interference covariance matrix; and    -   b) computing an estimate of a transmitted symbol on the basis of        the channel vector and the estimated x.

LIST OF DRAWINGS

Embodiments are described below, by way of example only, with referenceto the accompanying drawings, in which

FIG. 1 illustrates a wireless communication scenario to which someembodiments of the invention may be applied;

FIG. 2 illustrates a process for computing an interference rejectioncombining solution on a received signal according to an embodiment;

FIG. 3 illustrates a receiver architecture comprising some embodiments;

FIG. 4 illustrates a detailed procedure of a process for computing aninterference rejection combining solution by using a Krylov sub-spacepresentation; and

FIG. 5 illustrates a block diagram of a structure of an apparatusaccording to an embodiment.

DESCRIPTION OF EMBODIMENTS

The following embodiments are examples. Although the specification mayrefer to “an”, “one”, or “some” embodiment(s) in several locations, thisdoes not necessarily mean that each such reference is to the sameembodiment(s), or that the feature only applies to a single embodiment.Single features of different embodiments may also be combined to provideother embodiments. Furthermore, words “comprising” and “including”should be understood as not limiting the described embodiments toconsist of only those features that have been mentioned and suchembodiments may contain also features/structures that have not beenspecifically mentioned.

In the following, different exemplifying embodiments will be describedusing, as an example of an access architecture to which the embodimentsmay be applied, a radio access architecture based on long term evolutionadvanced (LTE Advanced, LTE-A) or new radio (NR, 5G), withoutrestricting the embodiments to such an architecture, however. A personskilled in the art will realize that the embodiments may also be appliedto other kinds of communications networks having suitable means byadjusting parameters and procedures appropriately. Some examples ofother options for suitable systems are the universal mobiletelecommunications system (UMTS) radio access network (UTRAN orE-UTRAN), long term evolution (LTE, the same as E-UTRA), wireless localarea network (WLAN or WiFi), worldwide interoperability for microwaveaccess (WiMAX), Bluetooth®, personal communications services (PCS),ZigBee®, wideband code division multiple access (WCDMA), systems usingultra-wideband (UWB) technology, sensor networks, mobile ad-hoc networks(MANETs) and Internet Protocol multimedia subsystems (IMS) or anycombination thereof

FIG. 1 depicts examples of simplified system architectures only showingsome elements and functional entities, all being logical units, whoseimplementation may differ from what is shown. The connections shown inFIG. 1 are logical connections; the actual physical connections may bedifferent. It is apparent to a person skilled in the art that the systemtypically comprises also other functions and structures than those shownin FIG. 1 .

The embodiments are not, however, restricted to the system given as anexample but a person skilled in the art may apply the solution to othercommunication systems provided with necessary properties.

The example of FIG. 1 shows a part of an exemplifying radio accessnetwork.

FIG. 1 shows terminal devices or user devices 100 and 102 configured tobe in a wireless connection on one or more communication channels in acell with an access node (such as (e/g)NodeB) 104 providing the cell.(e/g)NodeB refers to an eNodeB or a gNodeB, as defined in 3GPPspecifications. The physical link from a user device to a (e/g)NodeB iscalled uplink or reverse link and the physical link from the (e/g)NodeBto the user device is called downlink or forward link. It should beappreciated that (e/g)NodeBs or their functionalities may be implementedby using any node, host, server or access point etc. entity suitable forsuch a usage.

A communications system typically comprises more than one (e/g)NodeB inwhich case the (e/g)NodeBs may also be configured to communicate withone another over links, wired or wireless, designed for the purpose.These links may be used not only for signalling purposes but also forrouting data from one (e/g)NodeB to another. The (e/g)NodeB is acomputing device configured to control the radio resources ofcommunication system it is coupled to. The NodeB may also be referred toas a base station, an access point, an access node, or any other type ofinterfacing device including a relay station capable of operating in awireless environment. The (e/g)NodeB includes or is coupled totransceivers. From the transceivers of the (e/g)NodeB, a connection isprovided to an antenna unit that establishes bi-directional radio linksto user devices. The antenna unit may comprise a plurality of antennasor antenna elements. The (e/g)NodeB is further connected to core network110 (CN or next generation core NGC). Depending on the system, thecounterpart on the CN side can be a serving gateway (S-GW, routing andforwarding user data packets), packet data network gateway (P-GW), forproviding connectivity of user devices (UEs) to external packet datanetworks, or mobile management entity (MME), etc.

The user device (also called UE, user equipment, user terminal, terminaldevice, etc.) illustrates one type of an apparatus to which resources onthe air interface are allocated and assigned, and thus any featuredescribed herein with a user device may be implemented with acorresponding apparatus, such as a relay node. An example of such arelay node is a layer 3 relay (self-backhauling relay) towards the basestation. 5G specifications support at least the following relayoperation modes: out-of-band relay where different carriers and/or RATs(Radio access technologies) may be defined for an access link and abackhaul link; and in-band-relay where the same carrier frequency orradio resources are used for both access and backhaul links. In-bandrelay may be seen as a baseline relay scenario. A relay node is calledan integrated access and backhaul (IAB) node. It has also inbuiltsupport for multiple relay hops. IAB operation assumes a so-called splitarchitecture having CU and a number of DUs. An IAB node contains twoseparate functionalities: DU (Distributed Unit) part of the IAB nodefacilitates the gNB (access node) functionalities in a relay cell, i.e.it serves as the access link; and a mobile termination (MT) part of theIAB node that facilitates the backhaul connection. A Donor node (DUpart) communicates with the MT part of the IAB node, and it has a wiredconnection to the CU which again has a connection to the core network.In the multihop scenario, MT part (a child IAB node) communicates with aDU part of the parent IAB node.

The user device typically refers to a portable computing device thatincludes wireless mobile communication devices operating with or withouta subscriber identification module (SIM), including, but not limited to,the following types of devices: a mobile station (mobile phone),smartphone, personal digital assistant (PDA), handset, device using awireless modem (alarm or measurement device, etc.), laptop and/or touchscreen computer, tablet, game console, notebook, and multimedia device.It should be appreciated that a user device may also be a nearlyexclusive uplink only device, of which an example is a camera or videocamera loading images or video clips to a network. A user device mayalso be a device having capability to operate in Internet of Things(IoT) network which is a scenario in which objects are provided with theability to transfer data over a network without requiring human-to-humanor human-to-computer interaction. The user device may also utilizecloud. In some applications, a user device may comprise a small portabledevice with radio parts (such as a watch, earphones or eyeglasses) andthe computation is carried out in the cloud. The user device (or in someembodiments a layer 3 relay node) is configured to perform one or moreof user equipment functionalities. The user device may also be called asubscriber unit, mobile station, remote terminal, access terminal, userterminal or user equipment (UE) just to mention but a few names orapparatuses.

Various techniques described herein may also be applied to acyber-physical system (CPS) (a system of collaborating computationalelements controlling physical entities). CPS may enable theimplementation and exploitation of massive amounts of interconnected ICTdevices (sensors, actuators, processors microcontrollers, etc.) embeddedin physical objects at different locations. Mobile cyber physicalsystems, in which the physical system in question has inherent mobility,are a subcategory of cyber-physical systems. Examples of mobile physicalsystems include mobile robotics and electronics transported by humans oranimals.

Additionally, although the apparatuses have been depicted as singleentities, different units, processors and/or memory units (not all shownin FIG. 1 ) may be implemented.

5G enables using multiple input—multiple output (MIMO) antennas, manymore base stations or nodes than the LTE (a so-called small cellconcept), including macro sites operating in co-operation with smallerstations and employing a variety of radio technologies depending onservice needs, use cases and/or spectrum available. 5G mobilecommunications supports a wide range of use cases and relatedapplications including video streaming, augmented reality, differentways of data sharing and various forms of machine type applications(such as (massive) machine-type communications (mMTC), includingvehicular safety, different sensors and real-time control. SG isexpected to have multiple radio interfaces, namely below or at 6 GHz,cmWave and mmWave, and also being capable of being integrated withexisting legacy radio access technologies, such as the LTE. Integrationwith the LTE may be implemented, at least in the early phase, as asystem, where macro coverage is provided by the LTE and 5G radiointerface access comes from small cells by aggregation to the LTE. Inother words, 5G is planned to support both inter-RAT operability (suchas LTE-5G) and inter-RI operability (inter-radio interface operability,such as below 6 GHz—cmWave, below or at 6 GHz—cmWave—mmWave). One of theconcepts considered to be used in 5G networks is network slicing inwhich multiple independent and dedicated virtual sub-networks (networkinstances) may be created within the same infrastructure to run servicesthat have different requirements on latency, reliability, throughput andmobility.

The current architecture in LTE networks is fully distributed in theradio and typically fully centralized in the core network. Thelow-latency applications and services in 5G require to bring the contentclose to the radio which leads to local break out and multi-access edgecomputing (MEC). 5G enables analytics and knowledge generation to occurat the source of the data. This approach requires leveraging resourcesthat may not be continuously connected to a network such as laptops,smartphones, tablets and sensors. MEC provides a distributed computingenvironment for application and service hosting. It also has the abilityto store and process content in close proximity to cellular subscribersfor faster response time. Edge computing covers a wide range oftechnologies such as wireless sensor networks, mobile data acquisition,mobile signature analysis, cooperative distributed peer-to-peer ad hocnetworking and processing also classifiable as local cloud/fog computingand grid/mesh computing, dew computing, mobile edge computing, cloudlet,distributed data storage and retrieval, autonomic self-healing networks,remote cloud services, augmented and virtual reality, data caching,Internet of Things (massive connectivity and/or latency critical),critical communications (autonomous vehicles, traffic safety, real-timeanalytics, time-critical control, healthcare applications).

The communication system is also able to communicate with other networks112, such as a public switched telephone network or the Internet, orutilize services provided by them. The communication network may also beable to support the usage of cloud services, for example at least partof core network operations may be carried out as a cloud service (thisis depicted in FIG. 1 by “cloud” 114). The communication system may alsocomprise a central control entity, or a like, providing facilities fornetworks of different operators to cooperate for example in spectrumsharing.

Edge cloud may be brought into radio access network (RAN) by utilizingnetwork function virtualization (NFV) and software defined networking(SDN). Using edge cloud may mean access node operations to be carriedout, at least partly, in a server, host or node operationally coupled toa remote radio head or base station comprising radio parts. It is alsopossible that node operations will be distributed among a plurality ofservers, nodes or hosts. Application of cloudRAN architecture enablesRAN real time functions being carried out at the RAN side (in adistributed unit, DU 105) and non-real time functions being carried outin a centralized manner (in a centralized unit, CU 108).

It should also be understood that the distribution of functions betweencore network operations and base station operations may differ from thatof the LTE or even be non-existent. Some other technology advancementsprobably to be used are Big Data and all-IP, which may change the waynetworks are being constructed and managed. 5G (or new radio, NR)networks are being designed to support multiple hierarchies, where MECservers can be placed between the core and the base station or node B(gNB). It should be appreciated that MEC can be applied in 4G networksas well.

5G may also utilize satellite communication to enhance or complement thecoverage of 5G service, for example by providing backhauling. Possibleuse cases are providing service continuity for machine-to-machine (M2M)or Internet of Things (IoT) devices or for passengers on board ofvehicles, or ensuring service availability for critical communications,and future railway, maritime, and/or aeronautical communications.Satellite communication may utilize geostationary earth orbit (GEO)satellite systems, but also low earth orbit (LEO) satellite systems, inparticular mega-constellations (systems in which hundreds of(nano)satellites are deployed). Each satellite 109 in themega-constellation may cover several satellite-enabled network entitiesthat create on-ground cells. The on-ground cells may be created throughan on-ground relay node or by a gNB located on-ground or in a satellite.

It is obvious for a person skilled in the art that the depicted systemis only an example of a part of a radio access system and in practice,the system may comprise a plurality of (e/g)NodeBs, the user device mayhave an access to a plurality of radio cells and the system may comprisealso other apparatuses, such as physical layer relay nodes or othernetwork elements, etc. At least one of the (e/g)NodeBs or may be aHome(e/g)nodeB. Additionally, in a geographical area of a radiocommunication system a plurality of different kinds of radio cells aswell as a plurality of radio cells may be provided. Radio cells may bemacro cells (or umbrella cells) which are large cells, usually having adiameter of up to tens of kilometers, or smaller cells such as micro-,femto- or picocells. The (e/g)NodeBs of FIG. 1 may provide any kind ofthese cells. A cellular radio system may be implemented as a multilayernetwork including several kinds of cells. Typically, in multilayernetworks, one access node provides one kind of a cell or cells, and thusa plurality of (e/g)NodeBs are required to provide such a networkstructure.

For fulfilling the need for improving the deployment and performance ofcommunication systems, the concept of “plug-and-play” (e/g)NodeBs hasbeen introduced. Typically, a network which is able to use“plug-and-play” (e/g)Node Bs, includes, in addition to Home (e/g)NodeBs(H(e/g)nodeBs), a home node B gateway, or HNB-GW (not shown in FIG. 1 ).A HNB Gateway (HNB-GW), which is typically installed within anoperator's network may aggregate traffic from a large number of HNBsback to a core network.

As described in Background, it would be beneficial to reducecomputational complexity of an interference rejection combining (IRC)equalization receiver. The IRC receiver is conventionally applied toreceivers with multiple antennas and multiple spatial layers configuredbetween a transmitter and a receiver, e.g. a terminal device 100 and anaccess node 104. The receiver receives multiple beams or input streamsfrom the transmitter, one stream per receiver antenna element. Themultiple beams or input streams may together form one or more spatiallayers configured between the transmitter and the receiver. As known inthe art, the spatial layers are generated via MIMO processing andantenna arrays at both transmitter and receiver. In order to efficientlyutilize beamforming and realize the spatial layers, multiple antennaelements and respective beams may be configured per spatial layers inthe MIMO processing. Each spatial layer and the respective input streamsof the spatial layer may be then processed at a time, by considering thesignals from the other spatial layers as interference. The MIMO receiverprocessing may comprise reception beamforming in which a set of inputstreams per spatial layer are extracted from signals received by theantenna elements. The interference covariance matrix mentioned inBackground is then computed to represent the power of interference inthe set of streams and correlation of interference within the set ofinput streams of the spatial layer subjected to the IRC, and thereceiver computes an IRC solution that aims to reduce the interference.The IRC solution conventionally aims to whiten the interference whichinvolves computing an inverse of the covariance matrix. This computationis very complex, and it would be beneficial to reduce the complexity ofthe IRC receiver. A conventional IRC equalization solution is defined asŝ=(H ^(H) R ⁻¹ H+I)⁻¹ H ^(H) R ⁻¹ y   (1)where H ϵ

^(N×L) defines a channel matrix containing channel estimates for allantennas or input streams (and spatial layers), N defines the number ofantennas or equivalently beams or input streams, L defines the number ofspatial layers configured for the terminal device in the case ofsingle-user MIMO (SU-MIMO) and in the case of multi-user MIMO (MU-MIMO)L represents the total number of spatial layers over all scheduledterminal devices, R ϵ

^(N×N) defines the interference covariance matrix, and y ϵ

^(N×1) defines the received data samples. The interference covariancematrix may contain noise elements such as additive white Gaussian noiseand could equally be called an interference-plus-noise covariancematrix. An output of the IRC equalization solution is a vector oftransmitted symbol estimates ŝ.

In the embodiments described below, the IRC solution for the multiplespatial layers and multiple input streams is split into a single-layerIRC (SL-IRC) equalizer solution. The idea is that the IRC equalizationis computed per spatial layer, allowing to reduce the dimensions andcomputational complexity of the IRC equalization. This reduces therepresentation of Equation (1) into the following form:ŝ=(h ^(H) R−1 +1)⁻¹ h ^(H) R ⁻¹ y=(x^(H) h+1)⁻¹ x ^(H) y   (2)where h ϵ

^(N×1) defines the channel vector containing estimates for all antennasor beams or input streams for a specific spatial layer, and R definesthe interference (plus noise) covariance matrix for the spatial layerunder study. Accordingly, the channel matrix H reduces to a channelvector h and the output of the SL-IRC solution is an estimate of thetransmitted symbol ŝ for a specific layer, instead of a symbol vector.The received sample vector y may also be spatial-layer-specific, iflayer-specific beamforming has been applied. The interference covariancematrix also reduces to a matrix that represents the interference powerand interference correlation between input streams of the spatial layerunder the SL-IRC processing. In the conventional IRC solution, thecomputationally heavy part is the estimation of R⁻¹. This requirestechniques to firstly make the covariance matrix estimate invertible andthen inverting the matrix. A whitening-based IRC approach allows toavoid explicit inverse of R by using a Cholesky decomposition as awhitening matrix. Although significant savings in the processingcomplexity can be achieved, the approach is still too complex to allowpower-efficient, low latency SL-IRC equalization in the receiver.

The key to note in Equation (2) is that we are interested in solvingx=R⁻¹h from a system of linear equations Rx=h. Because R is Hermitian,we also have x^(H)=(R⁻¹h)^(H)=h^(H)R^(−H)=h^(H)R⁻¹, and we obtain thesecond term for SL-IRC shown above in Equation (2). Thanks to thesingle-layer processing, x^(H)h and x^(H)y reduces to a scalar and wecan use an approximation of x instead of an exact solution (see detailsfor approximating x below). This kind of problem presentation leads usto solving ŝ via Krylov sub-spaces that helps us in avoiding thecomputationally complex covariance matrix inversion. FIG. 2 illustratesan embodiment of a process for estimating an IRC equalization solutionby using a set of linear equations. The process may be executed in areceiver for the terminal device 100 or for the access node, or foranother radio receiver. The process may be executed by an apparatus forsuch a receiver, e.g. a chipset or at least one processor with at leastone memory.

Referring to FIG. 2 , the process comprises: acquiring (block 200) setof input streams associated with a spatial layer configured for aterminal device; estimating (block 202), on the basis of a referencesignal, a channel vector representing a radio channel responseassociated with the spatial layer; computing (block 202) an interferencecovariance matrix representing power of interference from at least oneother spatial layer in the set of input streams and correlation of theinterference within the set of input streams of the spatial layer;performing a per-layer interference rejection combining equalization onthe set of input streams, comprising: estimating x=R⁻¹h as a combinationof a set of linear equations, wherein the number of linear equations isdefined by an input parameter to be equal to or smaller than dimensionsof the interference covariance matrix; and computing an estimate of atransmitted symbol on the basis of the channel vector and the estimatedx.

After block 206, it may be determined whether or not there is anotherspatial layer for which no IRC solution has not yet been estimated. Forexample, upon carrying out blocks 200 to 206 for the set of inputstreams of one spatial layer, the blocks 200 to 206 may be carried outfor a second set of input streams of another spatial layer co-scheduledto the same time-frequency resources as the first spatial layer.

In an embodiment, the set of linear equations defines a Krylov sub-spacepresentation comprising orthonormal basis vectors defining the Krylovsub-space, wherein the input parameter defines the number of saidorthonormal basis vectors.

Using the Krylov sub-space presentation or another presentation based ona set of linear equations in the estimation of the transmitted symbol,the inversion of the covariance matrix can be avoided. This reducescomputational complexity of the IRC equalization by a substantialamount. The reduction depends on the total number of input streams perspatial layer, total number of co-scheduled spatial layers, and on themodulation and coding scheme, for example, but as much as 93 percent (%)less complex multiplications than a traditional solution based onEquation (1) and as much as 89% less complex multiplications than asolution using the whitening-based IRC can be realized. Advantages inthe computational complexity can be gained with the equal dimensions ofthe number set of linear equations and the dimensions of theinterference covariance matrix. Even further reduction in thecomputational complexity may be gained when the dimensions of the set oflinear equations (parameter m described below for the Krylov sub-space)are smaller than dimensions of the interference covariance matrix.

Multiple radio antenna streams or beams are typically associated witheach spatial layer, e.g. the first spatial layer and the second spatiallayer, as known in the art. As a consequence, each spatial layer maycomprise multiple input streams that define the dimensions of theinterference covariance matrix R and the length of the channel vector h.

The description below focuses on the Krylov sub-space for defining theset of linear equations. However, there exist other sub-spaces oralgorithms for solving the same problem, e.g., a biconjugate transposemethod.

Let us now take a closer look on the use of Krylov sub-spacepresentation in estimating the IRC solution. The embodiments describedbelow utilize a minimal residual method (MINRES), Lanczos algorithm, andThomas algorithm that are as such taught by the literature. Thefollowing description provides a disclosure for adapting such commonlyknown algorithms to the IRC equalization. The MINRES method is a methodthat approximates a solution by a vector in a Krylov sub-space with lowresidual error. The starting point is that we want to solve x from Ax=bwhich in the IRC solution would be represented as Rx=h. In other words,in the following notation A=R and b=h. For this, the m^(th) Krylovsubspace, K_(m), is defined asK _(m)(A,r ₀)=span{r ₀ , Ar ₀ , . . . , A ^(m−1) r ₀},where r₀=b−Ax₀ is the initial error given by our initial guess x₀. Thespan function follows its conventional mathematical definition. Becausethe vectors r₀, Ar₀, . . . , A^(m−1)r₀ are linearly dependent, forexample Lanczos algorithm may be used to find orthonormal basis V_(m)for K_(m). The algorithm described herein approximates the exactsolution of x=A⁻¹b, with a vector x_(m) ϵ K_(m) that provides asufficiently small estimation error r_(m)b−A(x₀+x_(m)). One aspect ofreducing the computational complexity is to select the number of basisvectors m to be sufficiently small while achieving sufficiently lowestimation error r_(m)=b−A(x₀+x_(m)). One aspect of defining thesufficiently low estimation error is that bit or block error rateperformance of a radio link between the transmitter and the receiver isnot compromised. Another aspect is that we can trade-off linkperformance and power consumption, e.g., in UE receiver we can usesmaller m-value to reduce power consumption in low-battery scenario. Wecan rewrite the vector x=x₀+x_(m)=x₀+V_(m)z, where x₀ is an initialguess, x_(m) is the approximate in K_(m)(A, r₀) and z ϵ

^(m) is a vector containing the linear combination weights for theorthonormal basis vectors.

The initial guess may be set to zero, x₀₌0 but, in another embodiment,x₀=h./diag(R), which defines that each element of the channel vector his divided with the corresponding diagonal element of R. It has beendiscovered that this initialization may provide improved performanceparticularly in the case of SL-IRC. As described above, the number oforthonormal basis vectors m defining the Krylov sub-space presentationis a parameter affecting the computation complexity. As described abovein connection with FIG. 2 , the value of m is selected to definedimensions of the Krylov sub-space to be smaller than dimensions of theinterference covariance matrix R. In practice, it means that m<N_(r),where N_(r) is the number of input streams in the spatial layersubjected to the SL-IRC estimation Embodiments for selecting m aredescribed below. The same principles apply to the other equivalentmethods for solving x from Rx=h, e.g., the biconjugate transpose method.

The Krylov presentation or, equivalently, an orthonormal Krylov subspacemay be created by using the Lanczos algorithm described in greaterdetail in the literature. As an output, a matrix, V_(m), containing them orthonormal basis vectors of the Krylov subspace are acquired.Furthermore, the Lanczos algorithm outputs real valued vectors α and β,that correspond to elements of the main diagonal (α) and firstsub-diagonals (β) of the symmetric tri-diagonal matrix H_(m),respectively. The first sub-diagonals of H_(m), are identical, as knownin connection with Lanczos algorithm. The Lanczos algorithm belongs to afamily of power methods for finding the eigenvalues and the orthonormaleigenvectors, and other embodiments may employ another power method. AnArnoldi iteration method is yet another potential algorithm.

Following the MINRES method, the next task is to solve X_(m)=V_(m)z, butfirst we have to solve

${\min\limits_{z}{{{H_{m}z} - {\gamma e_{1}}}}_{2}},$where γ=norm(r₀) is the vector norm of r₀, and e₁=[1,0, . . . ,0] is theidentity vector.

By noting the tri-diagonal structure of H_(m), the Thomas algorithm canbe used to directly solve z=H_(m) ⁻¹γe₁. At this point, an approximationis made that ∥H_(m)z−γe₁∥₂=0. H_(m) may be arranged to have only realvalues without impacting the link performance. This results from the useof the Lanczos algorithm. With finite precision arithmetics, complexvalues may appear but such values may be forced to be represented byusing only the real values. This allows to implement the Thomasalgorithm only for real values, thus reducing the computationalcomplexity.

Then, X_(m)=V_(m)z and the estimate x=x_(m)+x₀≈R⁻¹h are computed. Afterthis, solving the IRC solution is straightforward by following Equation(2). With the knowledge of x, the received signal y, and the channelvector h, the estimate of the transmitted symbols is computed and outputfor further processing in the receiver. The further processing mayinclude demodulation and decoding, for example.

FIG. 3 illustrates a processing chain or, equivalently, an architectureof a receiver for computing the SL-IRC solution described above.Referring to FIG. 3 , the channel vector h may be stored in a buffer300, the covariance matrix R may be stored in a buffer 320, and areceived data symbol vector y may be stored in a buffer 330. The channelvector may be subjected to an averaging operation in block 302, and thenumber of channel estimates to be averaged may be adaptive and afunction of determined parameters, e.g. a modulation and coding scheme(MCS) applied to the data symbols. In other embodiments, the averagingis omitted.

The Krylov sub-space basis vectors are generated in block 304, and thenumber of basis vectors is defined by the input parameter m. Asdescribed above, m may be smaller than the dimensions of the covariancematrix, e.g. the number of columns of the covariance matrix R. In anembodiment, m is dependent on at least one of a number of input streamsN_(r) in the set if input streams of the spatial layer under IRCprocessing, the MCS of the spatial layer subjected to the interferencerejection combining equalization, and a total number of spatial layersconfigured for the terminal device and, optionally, other terminaldevices in the same time-frequency resources. An access node mayschedule the same time-frequency resources but different spatial layersto multiple terminal devices. In an embodiment of FIG. 2 or 3 , m is afunction of a plurality of these parameters, or even all of them asdescribed below.

In an embodiment, m is dependent on the number of input streams in theset of input streams, the modulation and coding scheme of the spatiallayer subjected to the interference rejection combining equalization,and the number of spatial layers configured for the terminal device(s),and wherein values of the input parameter are directly proportional withan order of the modulation and coding scheme, directly proportional tothe number of spatial layers, and inversely proportional to the numberof input streams. The number of spatial layers may include all spatiallayers associated with the same time-frequency resource, e.g. they mayinclude spatial layers configured to the terminal device but they mayalso include one or more spatial layers scheduled to one or more otherterminal devices. The logic is that with a smaller number of spatiallayers, there is less interference and thus a smaller Krylov sub-spacecan provide sufficient performance. The same principle applies to theother sub-spaces or other sets of linear equations, e.g. the biconjugatetranspose method. Tables below illustrate some embodiments of dependenceof m on each of these parameters.

Number of Spatial Layers N_(L) Value of m 1 1 2 2 3 3 4 4 5 5 6 5 7 6 86

Number of Input Streams N_(B) Change to Value of m 8 +1 16 0 24 −1

Modulation and Coding Scheme Change to Value of m QPSK −3 16-QAM −164-QAM 0 256-QAM  +1

With respect to the modulation and coding schemes, QPSK means quadraturephase shift keying and QAM quadrature amplitude modulation. The numberbefore QAM means the number of symbols in the symbol constellation, asknown in the art. In a case where the number of spatial layers and atleast one of the number of input streams and the modulation and codingscheme is used for selecting the value of m, the number of spatiallayers may be used to define an initial value for m that may then beadapted on the basis of the modulation and coding scheme and/or thenumber of input streams by using the above-described logic. With lowernumber of input streams, the initial value may be increased while it maybe decreased with the greater number of input streams. With lower-ordermodulation and coding schemes such as the QPSK or 16-QAM, the initialvalue may be decreased, while it may be maintained or even increasedwith the high-order modulation schemes such as 64-QAM and 256-QAM. Sincethe number of spatial layers is common to all spatial layers subjectedto the IRC processing, that number may be equal to all spatial layers.However, variation in the value of m for the different spatial layersmay be introduced, if the spatial layers are configured with a differentnumber of input streams N_(r) and different modulation and codingschemes.

The dependence of m on the MCS may be expanded to dependence of m on acode rate of the spatial layer. The same logic as with the MCS mayapply, meaning that a smaller m may be selected if the code rate issmall (below a threshold) while a greater m may be selected for agreater code rate (above the threshold). Multiple thresholds may be usedin a case where m may assume more than two values, but the logicremains: the value of m is proportional to the value of the code rate.

As described above, the Krylov sub-space presentation output from block304 comprises elements of a real-valued tridiagonal matrix α and β, andwherein step b) comprises inversion of the real-valued tridiagonalmatrix H_(m).

$H_{m} = \begin{pmatrix}\alpha_{1} & \beta_{2} & \ldots & 0 & 0 \\\beta_{2} & \alpha_{2} & \beta_{3} & \ddots & 0 \\ \vdots & \beta_{3} & \alpha_{3} & \ddots & \vdots \\0 & \vdots & \ddots & \ddots & \beta_{m} \\0 & 0 & \ldots & \beta_{m} & \alpha_{m}\end{pmatrix}$

In order to solve z (the weights for the orthonormal basis vectors), asdescribed above, the matrix H_(m) needs to be inverted. Thanks to beingreal-valued and having reduced dimensions, it is much less complex thaninverting the complex-valued interference covariance matrix. In anembodiment the inversion of the real-value tridiagonal matrix is carriedout when solving weights for the orthonormal basis vectors by using theThomas algorithm. Alternative solution is to use, e.g., an eigen valuedecomposition on matrix H_(m), and build estimate on z by using aspecific number of eigen vectors and inverted eigen values to representinverse of H_(m). As known in the art, the Thomas algorithm solves zfrom H_(m)z=d where d=γe₁, as described above. In the case of m=1, z issolved as

$z = {\frac{\gamma}{\alpha_{1}}.}$After solving the weights for the orthonormal basis vectors defining theKrylov sub-space presentation, we can solve x, as described above (block306). Following Equation (2) and FIG. 3 , Hermitian transpose of x isthen multiplied with the channel vector in block 308. The result, x^(H)hcan be assumed to be real-valued to reduce memory consumption and toreduce computational complexity in the following interpolation steps.Then, both x and x^(H)h are subjected to time-domain andfrequency-domain interpolation in blocks 310 and 312, respectively. Thepurpose of the interpolation is to estimate values of x (or equivalentlyx^(H)) and x^(H)h for all sub-carriers and all time-domain signals (orsamples) carrying a data symbol y. As known in the art, demodulationreference symbols (DMRS) are transmitted only on certain (not all)sub-carriers and/time-domain symbols. Therefore, the estimates of xapply only to those sub-carriers and time-domain symbols and may beinterpolated to the other sub-carriers and time-domain symbols in blocks310 and 312. One advantage of this architecture is, in addition to thosedescribed above, that the Lanczos algorithm, (tridiagonal) matrixinversion, and computation of x^(H)h is performed before theinterpolation blocks. As a consequence, the number of sub-spaceprocessing calls and following samples subjected to the inversion, andnumber of vector products required to solve x^(H)h, is much smaller thanin a case where the inversion was performed after the interpolation. Asa consequence, low computational complexity can be achieved.

Following again Equation (2), the Hermitian transpose of estimate of xis then multiplied with the received signal sample y in block 314.Thereafter, the remaining operations of Equation (2) are performed inblock 316, thus acquiring the IRC estimate of the transmitted symbol.

FIG. 4 illustrates a detailed flow diagram of the procedure and let usdisclose some further embodiments with reference to FIG. 4 . Afterblocks 200 and 202, or in parallel with them, at least some parametersof the algorithm are initialized in block 400. The parameter initializedin block 400 may include at least one of the following parameters: thedimensions of the Krylov sub-space m, the initial estimate xo, and theaveraging parameter input to block 302.

As described, above, the initial estimate xo may be initialized as zeroor as x₀=h./diag(R) where ./ represents element-wise division operation.

In an embodiment, the averaging parameter is a function of themodulation and coding scheme, similarly to m. The dependence of theaveraging parameter on the modulation and coding scheme may follow alogic where parameter value is smaller for a first modulation schemethan for a second modulation scheme, wherein the first modulation schememaps a greater number of bits per symbol than the second modulationscheme. In other words, the averaging parameter is smaller for ahigher-order modulation scheme such as 64-QAM or 256-QAM than for alower-order modulation scheme such as QPSK or 16-QAM. Table belowillustrates an embodiment of the dependence. The same principle appliesto the other sub-spaces or other sets of linear equations, e.g. thebiconjugate transpose method.

Modulation and Coding Scheme Averaging Parameter Value QPSKN_(channelEstimatePerPRB) 16-QAM N_(channelEstimatePerPRB)/2 64-QAMN_(channelEstimatePerPRB)/2 256-QAM  1

By including the layer-specific code rate information to the MCS table,even more accurate control on the value of averaging parameter can beachieved. For example, if the code rate with 64-QAM is larger than 0.8,the averaging parameter value is set to N_(channelEstimatePerPRB)/3.

The averaging may be performed per physical resource block (PRB) withN_(channelEstimatePerPRB) channel estimates, i.e. the averaging may beperformed over channel estimates in the frequency domain within the PRB.As known in the art, the PRB may comprise a determined number offrequency resource elements (e.g. sub-carriers). As illustrated in theTable, when the modulation and coding scheme is of low order such as theQPSK, N_(channelEstimatePerPRB) channel estimates may be averaged. In anembodiment, that all channel estimates of the PRB are averaged in thecase of QPSK. With medium-order modulation and coding schemes such as16-QAM and 64-QAM, N_(channelEstimatePerPRB)/2 channel estimates may beaveraged, and the averaging may be omitted for a high-order modulationand coding scheme such as 256-QAM. Accordingly, the computationalcomplexity can be reduced while maintaining acceptable performance. Asdescribed above and illustrated in FIG. 3 , the averaging may beperformed before computing x.

The parameters to be initialized may depend on the embodiment, e.g.whether or not to perform the above-described averaging of channelestimates. In embodiments that do not support the averaging of channelestimates, the respective initialization of the averaging parameter maynaturally be omitted. Similarly, if the initial estimate is fixed, e.g.x₀=0, the initialization may be void of computations and simplify into amemory retrieval.

In block 402, the Krylov sub-space orthonormal basis vectors aregenerated for a spatial layer under processing (see also block 304),e.g., by using the Lanczos method or another power method, based on thechannel vector and interference covariance matrix. Then, the weights forthe basis vectors may be computed by using the Thomas algorithm, forexample. Thereafter, x may be solved in block 406 (see also block 306),and block 406 may comprise combining the orthonormal basis vectors withrespective weights. Then, the final SL-IRC estimate may be computed inblock 408 where the weights are combined with the respective orthonormalbasis vectors and with an initial estimate. Block 408 may be repeated(via block 409) to other symbols of the spatial layer. As describedabove, the interpolation spans the estimate of x or a parameter derivedfrom x (e.g. x^(H)h) to the other time-frequency resource (sub-carriersand/or time-domain symbols). As a consequence, IRC estimates of thevalues of data symbols transmitted on the respective time-frequencyresources of the same spatial layer may be computed by repeating block408. In block 410, it is determined whether or not there is a spatiallayer still to be processed. If there is, the process returns to block402 where the next spatial layer and the respective input streams aretaken into the processing. If all the spatial layers have beenprocessed, the process may end.

It should be appreciated that the sequential order of processing symbolswithin a spatial layer and processing spatial layers (arrangement ofblocks 409 and 410) may be various. The different spatial layers may beprocessed even in parallel by different processing circuitries, forexample.

FIG. 5 illustrates an apparatus according comprising a processingcircuitry 50, such as at least one processor, and at least one memory 60including a computer program code (software) 64, wherein the at leastone memory and the computer program code (software) are configured, withthe at least one processor, to cause the apparatus to carry out theprocess of FIG. 2 or any one of its embodiments described above. Theapparatus may be for the terminal device 100 or for the access node 104,e.g. for the DU or CU. The apparatus may be a circuitry or an electronicdevice realizing some embodiments of the invention in the terminaldevice or the access node. The apparatus carrying out theabove-described functionalities may thus be comprised in such a device,e.g. the apparatus may comprise a circuitry such as a chip, a chipset, aprocessor, a micro controller, or a combination of such circuitries forthe terminal device or the access node. In other embodiments, theapparatus is generally for a radio device, e.g. the radio device or acircuitry in or designed to operate in the radio device.

The memory 60 may be implemented using any suitable data storagetechnology, such as semiconductor-based memory devices, flash memory,magnetic memory devices and systems, optical memory devices and systems,fixed memory and removable memory.

The processing circuitry 50 may comprise a SL-IRC processing circuitry52 configured to carry out the IRC estimation on the received inputstreams according to any one of the above-described embodiments. TheSL-IRC processing circuitry 52 may comprise a linear equationsgeneration circuitry 54 configured to generate the basis vectors andrespective weights for the basis vectors or the sets of linear equationsto approximate x. The SL-IRC processing circuitry may further comprise aSL-IRC solution estimation circuitry configured to compute the SL-IRCsolution by using the sub-space presentation or the sets of linearequations received from the circuitry 54. The SL-IRC circuitry mayfurther comprise at least some further components or functions from thearchitecture illustrated in FIG. 3 and described in the embodimentsabove.

In an embodiment, the apparatus further comprises a radio transceiver 62with multiple antenna elements for receiving the input streams for theIRC processing. The radio transceiver 62 may further comprise otherconventional radio receiver components such as filters, amplifiers,frequency-converters and base band signal processing components andfunctions.

As used in this application, the term ‘circuitry’ refers to one or moreof the following: (a) hardware-only circuit implementations such asimplementations in only analog and/or digital circuitry; (b)combinations of circuits and software and/or firmware, such as (asapplicable): (i) a combination of processor(s) or processor cores; or(ii) portions of processor(s)/software including digital signalprocessor(s), software, and at least one memory that work together tocause an apparatus to perform specific functions; and (c) circuits, suchas a microprocessor(s) or a portion of a microprocessor(s), that requiresoftware or firmware for operation, even if the software or firmware isnot physically present.

This definition of ‘circuitry’ applies to uses of this term in thisapplication. As a further example, as used in this application, the term“circuitry”would also cover an implementation of merely a processor (ormultiple processors) or portion of a processor, e.g. one core of amulti-core processor, and its (or their) accompanying software and/orfirmware. The term “circuitry” would also cover, for example and ifapplicable to the particular element, a baseband integrated circuit, anapplication-specific integrated circuit (ASIC), and/or afield-programmable grid array (FPGA) circuit for the apparatus accordingto an embodiment of the invention. The processes or methods described inFIG. 3 or any of the embodiments thereof may also be carried out in theform of one or more computer processes defined by one or more computerprograms. The computer program(s) may be in source code form, objectcode form, or in some intermediate form, and it may be stored in somesort of carrier, which may be any entity or device capable of carryingthe program. Such carriers include transitory and/or non-transitorycomputer media, e.g. a record medium, computer memory, read-only memory,electrical carrier signal, telecommunications signal, and softwaredistribution package. Depending on the processing power needed, thecomputer program may be executed in a single electronic digitalprocessing unit or it may be distributed amongst a number of processingunits.

The processes or methods described in FIGS. 2 to 4 , or any of theembodiments thereof may also be carried out in the form of one or morecomputer processes defined by one or more computer programs. Thecomputer program(s) may be in source code form, object code form, or insome intermediate form, and it may be stored in some sort of carrier,which may be any entity or device capable of carrying the program. Suchcarriers include transitory and/or non-transitory computer media, e.g. arecord medium, computer memory, read-only memory, electrical carriersignal, telecommunications signal, and software distribution package.Depending on the processing power needed, the computer program may beexecuted in a single electronic digital processing unit or it may bedistributed amongst a number of processing units. References tocomputer-readable program code, computer program, computer instructions,computer code etc. should be understood to express software for aprogrammable processor such as programmable content stored in a hardwaredevice as instructions for a processor, or as configured or configurablesettings for a fixed function device, gate array, or a programmablelogic device.

Embodiments described herein are applicable to wireless networks definedabove but also to other wireless networks. The protocols used, thespecifications of the wireless networks and their network elementsdevelop rapidly. Such development may require extra changes to thedescribed embodiments. Therefore, all words and expressions should beinterpreted broadly and they are intended to illustrate, not torestrict, the embodiment. It will be obvious to a person skilled in theart that, as technology advances, the inventive concept can beimplemented in various ways. Embodiments are not limited to the examplesdescribed above but may vary within the scope of the claims.

The invention claimed is:
 1. An apparatus comprising: at least oneprocessor; and at least one memory including computer program code that,when executed by the at least one processor, cause the apparatus toperform: acquiring set of input streams associated with a spatial layerconfigured for a terminal device; estimating, on the basis of areference signal, a channel vector h representing a radio channelresponse associated with the spatial layer; computing an interferencecovariance matrix R representing power of interference from at least oneother spatial layer in the set of input streams and correlation of theinterference within the set of input streams of the spatial layer;performing a per-layer interference rejection combining equalization onthe set of input streams, comprising: a) estimating x=R⁻¹h as acombination of a set of linear equations, wherein the number of linearequations is defined by an input parameter to be equal to or smallerthan dimensions of the interference covariance matrix; and b) computingan estimate of a transmitted symbol on the basis of the channel vectorand the estimated x.
 2. The apparatus of claim 1, wherein the inputparameter is dependent on at least one of a number of input streams inthe set of input streams, a modulation and coding scheme of the spatiallayer, and a total number of spatial layers configured for all terminaldevices scheduled to the same time-frequency resources as the terminaldevice.
 3. The apparatus of claim 2, wherein the input parameter isdependent on the number of input streams, the modulation and codingscheme of the spatial layer, and the total number of spatial layers, andwherein values of the input parameter are directly proportional with anorder of the modulation and coding scheme, directly proportional to thenumber of spatial layers, and inversely proportional to the number ofinput streams.
 4. The apparatus of claim 1, wherein the set of linearequations defines a Krylov sub-space presentation comprising orthonormalbasis vectors defining the Krylov sub-space, wherein the input parameterdefines the number of said orthonormal basis vectors.
 5. The apparatusof claim 4, wherein the Krylov sub-space presentation further compriseselements of a real-valued tridiagonal matrix, and wherein step b)comprises inversion of the real-valued tridiagonal matrix.
 6. Theapparatus of claim 5, wherein the at least one memory and computerprogram code are further configured, with the at least one processor, tocause the apparatus to perform the inversion of the real-valuetridiagonal matrix when solving weights for the orthonormal basisvectors by using Thomas algorithm, to combine the weights with therespective orthonormal basis vectors and with an initial estimate, andto compute the estimate of the transmitted symbol on the basis of saidcombining.
 7. The apparatus of claim 5, wherein the at least one memoryand computer program code are further configured, with the at least oneprocessor, to cause the apparatus to perform the inversion of thereal-value tridiagonal matrix when solving weights for the orthonormalbasis vectors by computing an eigenvalue decomposition of thetridiagonal matrix, to compute the weights by inverting eigenvalues ofthe eigenvalue decomposition, to combine the weights with the respectiveorthonormal basis vectors and with an initial estimate, and to computethe estimate of the transmitted symbol on the basis of said combining.8. The apparatus of claim 6, wherein the at least one memory andcomputer program code are further configured, with the at least oneprocessor, to cause the apparatus to use the initial estimatex₀=h./diag(R) in step b), wherein ./ represents element-wise divisionoperation.
 9. The apparatus of claim 4, wherein the at least one memoryand computer program code are further configured, with the at least oneprocessor, to cause the apparatus to generate the Krylov sub-spacepresentation by using Lanczos algorithm.
 10. The apparatus of claim 1,where the at least one memory and computer program code are furtherconfigured, with the at least one processor, to cause the apparatus tointerpolate the estimated x or a parameter derived from x totime-frequency resources not carrying the reference signal.
 11. Theapparatus of claim 1, wherein the at least one memory and computerprogram code are further configured, with the at least one processor, tocause the apparatus to average a determined number of channel estimates,wherein the determined number is a function of a modulation and codingscheme associated with the spatial layer.
 12. The apparatus of claim 11,wherein the determined number is smaller for a first modulation schemethan for a second modulation scheme, wherein the first modulation schememaps a greater number of bits per symbol than the second modulationscheme.
 13. A computer-implemented method for a radio receiver,comprising: acquiring set of input streams associated with a spatiallayer configured for a terminal device; estimating, on the basis of areference signal, a channel vector h representing a radio channelresponse associated with the spatial layer; computing an interferencecovariance matrix R representing power of interference from at least oneother spatial layer in the set of input streams and correlation of theinterference within the set of input streams of the spatial layer;performing a per-layer interference rejection combining equalization onthe set of input streams, comprising: a) estimating x=R⁻¹h as acombination of a set of linear equations, wherein the number of linearequations is defined by an input parameter to be equal to or smallerthan dimensions of the interference covariance matrix; and b) computingan estimate of a transmitted symbol on the basis of the channel vectorand the estimated x.
 14. A computer program product embodied on anon-transitory computer-readable medium and comprising a computerprogram code readable by a computer, wherein the computer program codeconfigures the computer to carry out a computer process comprising:acquiring set of input streams associated with a spatial layerconfigured for a terminal device; estimating, on the basis of areference signal, a channel vector h representing a radio channelresponse associated with the spatial layer; computing an interferencecovariance matrix R representing power of interference from at least oneother spatial layer in the set of input streams and correlation of theinterference within the set of input streams of the spatial layer;performing a per-layer interference rejection combining equalization onthe set of input streams, comprising: a) estimating x=R⁻¹h as acombination of a set of linear equations, wherein the number of linearequations is defined by an input parameter to be equal to or smallerthan dimensions of the interference covariance matrix; and b) computingan estimate of a transmitted symbol on the basis of the channel vectorand the estimated x.